Stream-based Hebbian Eigenfilter for real-time neuronal
spike discrimination
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Citation
Yu, Bo et al. “Stream-based Hebbian Eigenfilter for Real-time
Neuronal Spike Discrimination.” BioMedical Engineering OnLine
11.1 (2012): 18. Web.
As Published
http://dx.doi.org/10.1186/1475-925X-11-18
Publisher
BioMed Central Ltd
Version
Final published version
Accessed
Fri May 27 00:35:14 EDT 2016
Citable Link
http://hdl.handle.net/1721.1/71767
Terms of Use
Creative Commons Attribution
Detailed Terms
http://creativecommons.org/licenses/by/2.0
Yu et al. BioMedical Engineering OnLine 2012, 11:18
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RESEARCH
Open Access
Stream-based Hebbian eigenfilter for real-time
neuronal spike discrimination
Bo Yu1, Terrence Mak2,3*, Xiangyu Li1, Leslie Smith4, Yihe Sun1 and Chi-Sang Poon5
* Correspondence: terrence.
mak@ncl.ac.uk
2
School of Electrical, Electronic and
Computer Engineering, Newcastle
University, Newcastle upon Tyne
NE47RU, UK
Full list of author information is
available at the end of the article
Abstract
Background: Principal component analysis (PCA) has been widely employed for
automatic neuronal spike sorting. Calculating principal components (PCs) is
computationally expensive, and requires complex numerical operations and large
memory resources. Substantial hardware resources are therefore needed for
hardware implementations of PCA. General Hebbian algorithm (GHA) has been
proposed for calculating PCs of neuronal spikes in our previous work, which
eliminates the needs of computationally expensive covariance analysis and
eigenvalue decomposition in conventional PCA algorithms. However, large memory
resources are still inherently required for storing a large volume of aligned spikes for
training PCs. The large size memory will consume large hardware resources and
contribute significant power dissipation, which make GHA difficult to be
implemented in portable or implantable multi-channel recording micro-systems.
Method: In this paper, we present a new algorithm for PCA-based spike sorting
based on GHA, namely stream-based Hebbian eigenfilter, which eliminates the
inherent memory requirements of GHA while keeping the accuracy of spike sorting
by utilizing the pseudo-stationarity of neuronal spikes. Because of the reduction of
large hardware storage requirements, the proposed algorithm can lead to ultra-low
hardware resources and power consumption of hardware implementations, which is
critical for the future multi-channel micro-systems. Both clinical and synthetic neural
recording data sets were employed for evaluating the accuracy of the stream-based
Hebbian eigenfilter. The performance of spike sorting using stream-based eigenfilter
and the computational complexity of the eigenfilter were rigorously evaluated and
compared with conventional PCA algorithms. Field programmable logic arrays
(FPGAs) were employed to implement the proposed algorithm, evaluate the
hardware implementations and demonstrate the reduction in both power
consumption and hardware memories achieved by the streaming computing
Results and discussion: Results demonstrate that the stream-based eigenfilter can
achieve the same accuracy and is 10 times more computationally efficient when
compared with conventional PCA algorithms. Hardware evaluations show that 90.3%
logic resources, 95.1% power consumption and 86.8% computing latency can be
reduced by the stream-based eigenfilter when compared with PCA hardware. By
utilizing the streaming method, 92% memory resources and 67% power
consumption can be saved when compared with the direct implementation of GHA.
Conclusion: Stream-based Hebbian eigenfilter presents a novel approach to enable
real-time spike sorting with reduced computational complexity and hardware costs.
This new design can be further utilized for multi-channel neuro-physiological
experiments or chronic implants.
© 2012 Yu et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons
Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in
any medium, provided the original work is properly cited.
Yu et al. BioMedical Engineering OnLine 2012, 11:18
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Keywords: Brain-machine interface, Spike sorting, Hebbian eigenfilter, Hardware,
Principal component analysis
Background
Recently, multi-electrode arrays (MEAs) have become increasingly popular for neurophysiological experiments in vivo [1-4] or in vitro [5-8]. Compared with other methods
of signal acquisition, such as Electroencephalography (EEG) [9] and Electrocorticographical (ECoG) [10], MEAs provide the capability of recording neuronal spikes from
specific regions of the brain with high signal-to-noise ratio [1,5]. The substantial temporal and spatial resolutions provided by MEAs facilitate the studies of neural network
dynamic [11], plasticity [12], learning and information processing [13] and the developments of high performance brain-machine interface (BMI) for emerging applications,
such as motor rehabilitation for paralyzed or stroke patients [14-16].
Neuronal spike trains recorded by electrodes encompass noises introduced by measurement instruments, interferences from other vicinity neurons and action potentials
from unknown number of neurons. Neural signal processing that extracts useful information from noisy spike trains is necessary for spike information decoding and neural
network analysis in subsequent processes. In most MEA based systems, especially the
MEA based brain-machine interface (BMI), spike sorting that discriminates neuronal
spikes to corresponding neurons is among the very first steps of signal processing
[17-19] and its correctness significantly affects the reliability of the subsequent analysis
[20].
PCA-based spike sorting
Principal component analysis (PCA) is an effective and automatic spike sorting
method. PCA-based spike sorting calculates principal components (PCs) of a group of
neuronal spikes, and uses the first 2 or 3 PCs to constitute a feature space. Most variance of spikes can be captured by the feature space. When projecting neuronal spikes
into the feature space, inherent characters of neuronal spikes are highlighted, and several clusters composed by different neuronal spikes can be observed and differentiated.
A complete PCA-based spike sorting flow, including spike detection, peak alignment,
PCA-based feature extraction, and clustering is illustrated by Figure 1. Firstly, spike
detection [21,22] distinguishes neuronal spikes from background noises according to a
pre-trained threshold. Detected high dimensional spikes are then aligned at their peak
point for the PCA. PCs of aligned neuronal spikes that are orthogonal to each other
Figure 1 The procedure of PCA-based spike sorting.
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can be obtained through PCA-based feature extraction. The first two or three PCs are
used to constitute a low dimensional feature space. Aligned spikes are projected into
the feature space by the dot production between spikes and each PC. In the feature
space, dots represent aligned neuronal spikes and each cluster represents a prospective
neuron. At last, clustering algorithms are employed to differentiate clusters in the
feature space and assign dots (spikes) to their closest cluster (neuron).
Calculating PCs requires computationally expensive operations, including covariance
matrix calculation and eigenvalue decomposition. Besides, a large volume of neuronal
spikes needs to be temperately stored for training PCs. Large size memories are therefore required. While large computational complexity and memory usage are not issues
for recording and analysis of 100 channel systems [23], they are critical concerns for
systems with large number of channels (> 1000), and especially for implantable systems, which have tight constraints of hardware size and power consumptions.
GHA for calculating PCs of neuronal spikes
In our previous work [24], general Hebbian algorithm (GHA), so-called Hebbian eigenfilter, which presents an efficient approach for realizing PCA, was proposed for calculating
the leading PCs of neuronal spikes. Let x(i) , i Î [1, n] be n aligned spikes. Each aligned
spike is d dimension (containing d sample points), i.e. x(i) = x1 (i),x2 (i), ..., xd (i) T . Let l
be the dimension of feature space (the number of extracted principal components), h be
T
1 (j), W
2 (j), ..., W
d (j) be a l × d synaptic weight matrix
the learning rate, W(j)
= W
, and j be the iteration index. GHA for calculating the first l
that is initialized to W(1)
principal components of n aligned neuronal spikes is summarized in Table 1. Step 1 initia , is
lizes synaptic weights and the learning rate. The mean vector of n aligned spikes, μ
calculated in Step 2. After the mean vector is available, the mean vector is subtracted from
Table 1 GHA-basedspike feature extraction
Input:
Neuronal spikes,
x(i) ;
Initial synaptic weight,
x(i);
Learning rate, h ;
Output:
Principal components of neuronal spikes,
1. Initialize synaptic weight
;
W(N)
x(i)and learning rate h, j = 1
2. Calculate the mean vector of the aligned spikes
μ
=
n
i=1
x(i)/n
3. Zero-mean transformation
x(i) = x(i) − μ
1≤i≤n
4. Perform Hebbian learning on zero-mean data
x(i)
y(j) = W(j)
LT(j) = LT y(j)yT (j)
dW(j) = η y(j)xT (i) − LT(j)W(j)
+ 1) = W(j)
W(j
+ dW(j)
5. If j= N, the algorithm stops, otherwise j = j+ 1, go to step 4
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all aligned spikes in Step 3. After that, iteration learning will be performed on zero-mean
is an operator that sets all the elements above the
spikes. In the iteration learning, LT m
diagonal of matrix, m
, to zeros. The algorithm stops when the iteration step, j, equals to
will converge to the
N. If N is large enough and the learning rate is appropriate [25], W(j)
l most significant principal components of input spikes.
Compared with conventional PCA algorithms, GHA does not involve complicated
matrix computations, such as covariance matrix calculation and eigenvalue decomposition. Also, the algorithm has the ability to filter a specified number of most significant
PCs. Since most variances of aligned spikes are captured by the first few PCs, computing the leading PCs can effectively reduce a lot of computational efforts.
Although GHA eliminates computationally expensive operations, large memory
resources are still required in the training procedure. Large size hardware memories
consume significant hardware resources and power, which makes GHA impractical for
systems with tight constraints on hardware resources and power consumption.
In this paper, a new algorithm, namely stream-based Hebbian eigenfilter, is proposed
to mitigate the problem associated with the large memory required in the training procedure. Neural signals can be regarded as pseudo-stationary in considering of a short
recording period and relatively stable recording condition. The stream-based algorithm
exploits the pseudo-stationary characteristic of neural spikes and, thus eliminates the
need for temporary storage in the Hebbian learning. In order to justify the streaming
method and evaluate the performance of the stream-based eigenfilter, both clinical and
synthetic spike trains were used in this study. The accuracy of spike sorting using the
stream-based Hebbian eigenfilter was evaluated by comparing with conventional PCA
algorithms. The improvements in memory size and power consumption were rigorously evaluated using FPGA devices. The hardware performance of our method was
also compared with FPGA-based PCA. Evaluation results show that our proposed
approach mitigates the expensive hardware requirement of PCA, and further enables
real-time multi-channel recording systems and future BMI systems.
Method
Stream-based Hebbian eigenfilter
As shown in the definition of GHA-based feature extraction (Table 1), Hebbian learning
is defined to perform on a group of spikes of which mean is zero. Since zero-mean transformation cannot start until the mean is available, memories are required to temporarily
store all the aligned spikes when computing the mean vector. Therefore, the same set of
neuronal spikes can be used in the subsequent zero-mean transformation and Hebbian
learning. The memory size needed for buffering aligned spikes can be formulated by Eq.
1, where n is the number of spikes for learning, d is the number of sample points of
each spike, and w is the hardware word length of each sample point. For a quantitative
estimation of the memory requirement, we chose values of these parameters based on
commonly used recording and training conditions [19,26]. 25 KHz of sampling rate and
64 sampling points per spikes (each spike spans around 2.5 ms) were used for our estimation. In general, thousands neuronal spikes are used for training PCs [19]. Suppose
that the number of neuronal spikes for training is 1024, and each sample is 16 bits, 1 million bits memories are required for storing spikes. Note that this is only for one channel
training. Even larger memories are required for the multi-channel scheme.
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Memspikes = n × d × w
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(1)
Memory resources are expensive in terms of hardware design, especially for implantable or portable applications. Large size memory will consume large portions of hardware resources in hardware constrained systems. Reducing storage resources allows
integrating more computing resources in a single device, and further enables parallel
processing for a large number of channels at the same time. In addition, large memories contribute significant power consumption and thermal dissipation of hardware,
which should be minimized for implantable or portable applications. In this section,
we proposed a method, so-called stream-based Hebbian eigenfilter, to reduce the extremely large memory associated with Hebbain training by utilizing the pseudo-stationary
property of neuronal spikes.
Recorded neural signals have non-stationary nature which is mainly due to the relative movements between the recording electrodes and the recorded neurons. Also, the
magnitude of spike could change during excitation block or post inhibitory rebound
excitation or spike frequency adaptation, and the shape of the spike could change
when other ion channels are recruited, such as calcium-dependent potassium channels.
However, neural signals can be regarded as pseudo-stationary in considering of a short
recording period and relatively stable condition, simply because the chance of disturbance is small.
During a period of time, in which pseudo-stationarity exists, the shape of a neuronal
spike stays relatively fixed and can only be disturbed by various noises. This similarity
in recorded neuronal signals can be utilized to reduce the temporary storage requirement. That the same operation performed on signals from different recording periods
can lead to similar results due to the similarity of signals. For mean calculation, it
means that mean values of spikes from different recording periods are similar under
the pseudo-stationary property. Hebbian eigenfilter can use the mean vector obtained
from the previous recording period as an approximate mean of current spikes when
performing zero-mean transformation and Hebbian learning. Therefore, there is no
need to store a certain subset of data for both mean calculation and zero-mean transformation, and the corresponding memory requirement is eliminated.
The algorithm of stream-based Hebbian eigenfilter for spike sorting is presented in
Table 2. It has the same initialization scheme with the non-streaming algorithm, and
then calculates the mean vector of n neuronal spikes (step 2 in Table 2). Different
from the non-streaming algorithm for spike sorting, the spikes for mean calculation
are discarded after use. After mean calculation, zero-mean transformation and Hebbian
learning are performed on the obtained mean vector and the subsequent spikes (step 3
and 4 in Table 2). Since mean calculation and zero-mean transformation are performed on different data sets, there is no explicit storing requirement associated with
mean operations and Hebbian learning in the stream-based algorithm.
Evaluation method
Stream-based Hebbain eigenfilter uses data sets from different recording periods for mean
calculation and Hebbian learning. It is an approximate method based on the precondition
of pseudo-stationarity of neuronal spikes. In order to justify the pseudo-stationarity, we
evaluated the discrepancy in mean and PCs obtained by stream-based eigenfilter and
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Table 2 Algorithm of stream-based Hebbian Eigenfilter for spike sorting
Input:
Neuronal spikes,
x(i) ;
x(i);
Initial synaptic weight,
Learning rate, h;
Output:
;
W(N)
x(i)and learning rate h, j = 1
Principal components of neuronal spikes,
1. Initialize synaptic weight
2. Calculate the mean vector of n aligned spikes
a. i= 1,
μ
=0
=μ
+ x(i)
x(i)arrives μ
,
and
go
to step 3. Otherwise i = i + 1, go to Step 2.b
μ
= μ/n
b. When new spike
c. If i equals to n,
3. When new spike arrives, subtract the mean vector obtained from step 2
x(i) = x(i) − μ
i>n
4. Perform Hebbian x learning on
x(i)
x(i)
y(j) = W(j)
LT(j) = LT y(j)yT (j)
dW(j) = η y(j)xT (i) − LT(j)W(j)
+ 1) = W(j)
W(j
+ dW(j)
5. If j= N, the algorithm stops, otherwise j = j + 1, go to step 3
conventional PCA. In order to test the performance of the eigenfilter in the spike sorting
scenario, the accuracy of spike sorting using stream-based Hebbain eigenfilter was further
evaluated, and compared with that using conventional PCA algorithm. In addition, both
streaming and non-streaming eigenfilter were implemented on FPGAs to evaluate the
memory and power consumption reduced by utilizing the stream-based method.
Testing data
In order to verify the streaming method, realistic neuronal spike shapes, background
noises and vicinity neuronal interference should be taken into account in the evaluation. Both clinical data [27] and sophisticated synthetic spikes [27] were utilized for the
evaluation. These synthetic spike trains accurately model various background noises
and neuronal spikes profile that appear at single-channel clinical recordings.
For quantitatively evaluating the performance of the Hebbian spike sorting algorithm,
spike trains with known spike times and classifications should be employed. Clinical
extracellular recording with realistic spike shapes and noise interferences is one option
for qualitative studies. However, it is difficult to determine the precise classifications
and the source of the spike from clinical measurement and these are the “ground
truth” for any effective quantitative evaluation. Although these recordings can be
further manually annotated by experts, it has been shown that manually clustered
spikes have relative low accuracy and reliability [28]. For these reasons, synthetic spike
trains were utilized to quantify the performance of the proposed algorithm.
Both baseline [29] and sophisticated synthetic spike trains [27] were employed for
the quantitative evaluation. These benchmarks were used to maximize representative
different scenarios in real experiments. The baseline spike trains were generated from
spike synthesis tool [29]. The tool accurately models factors affecting extracellular
recordings, such as ion channels of the membrane, the electrical resistance and
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capacitance of the membrane, the extended spiking neural surface, back ground noises
and inference from other neurons, and provides an approximation of realistic clinical
data. Figure 2 shows both the clinical and synthetic spike shapes. More importantly,
parameters, such as the number of neurons contributing to the spike train, the waveform of neuronal spike, signal to noise ratio and the firing rate, can all be specified in
the tool. Through adjusting these parameters, various spike trains can be generated for
quantitative evaluations. For our evaluation, three groups of spike trains containing
two, three and four neurons were generated. White noise and artifacts noises contributed by background neurons were considered when generating noisy synthetic spike
trains. Each group contains spike trains with 11 different noise levels. The level of
noises is quantified by the SNR (signal-to-noise ratio). Under the same noise level, a
group of spike trains with neuron’s firing rate from 5 Hz to 50 Hz was generated. All
the data sets are 100 s in length and generated at a sampling rate of 25 KHz. These
spike trains provide ideal testing benchmarks to evaluate the proposed algorithm with
a variety of noise immunity and realistic background noise. Because our method differentiates neuronal spikes according to spike profiles, it is not effective for bursting
spikes that appear as concatenated and with decreasing amplitude. Although bursting
spikes can be identified and ruled out with the help of inter-spike-interval histograms
and cross-correlograms, addressing how to combine these methods with our work is
beyond the scope of the paper. In this paper, we do not take bursting spikes into
account.
Figure 2 (a) Clinical and (b)synthetic spike waveform of two neurons [24].
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Accuracy evaluation
As shown in Table 2 stream-based algorithm uses the mean vector of one data set to
estimate the mean vector of the following spikes (belonging to another data set). This
approximation of mean calculation is based on pseudo-stationary property of neuronal
j be the mean vector of data
spikes. Let d be the dimensionality of the mean vector, μ
set j, and μj,i represents the i-th elements of the mean vector of data set j. We used
the difference (error) between mean vectors obtained from two different data sets to
justify the pseudo-stationarity and the approximation. The difference (error) of mean is
defined by Eq. 2. The value of the difference (error) indicates the accuracy of the
streaming method for mean estimation. The smaller the error is, the more accurate
2 can be accurately estimated from
the estimation is. When the difference is zero, μ
d
|μ1,i − μ2,i |
Errormean = i=1
.
d
i=1 |μ2,i |
d
Errormean =
|μ1,i − μ2,i |
d
i=1 |μ2,i |
i=1
(2)
Further, we evaluated the deviation between PCs obtained by the stream-based Hebbian eigenfilter and conventional PCA. For PCA-based spike sorting, the direction of
PCs determines the feature space that is critical to the accuracy of classification. We
therefore used the angle between synaptic weights and PCs to define the deviation
(error) between PCs obtained by eigenfilter and PCA, as shown in Eq. 3. In the equa are synaptic weights and PCs obtained by Hebbian and conventional
tion, W
and PC
PCA methods respectively. When the two vectors have the same direction or the opposite direction, the result will equal to zero. Otherwise a value in [0,1) is obtained.
(3)
ErrorPC = 1 − W.PC
Finally the accuracy of spike sorting using stream-based Hebbian eigenfilter was evaluated in our work. Besides Hebbian eigenfilter, NEO based detection algorithm [22]
and K-means clustering algorithm [30] were employed in our evaluation to complete
spike sorting algorithms. We used the true positive rate (TPR) and the false positive
rate (FPR) to evaluate the performance of our algorithm. The true positive rate is
defined by Eq. 4, where K is the number of estimated clusters, and Numcorrect_classified_spikes,i and Numspikes,i stand for the number of correctly classified spikes of neuron i
and the total number of spikes of neuron i, respectively.
1 Numcorrect classified spikes;i
K
Numspikes;i
K
TPR =
(4)
i=1
The false positive rate is defined by Eq. 5, where Numfalse_classified_spikes,i and Numfalse_spikes,i stand for the number of false spikes (not belonging to neuron i) assigned to
neuron i and the total number of false spikes for neuron i, respectively.
1 Numfalse classified spikes;i
K
Numfalse spikes;i
K
FPR =
i=1
(5)
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Computational complexity evaluation
In order to quantitatively evaluate the computational complexity, we used the number
of operations and hardware memories required by an algorithm in the study. By comparing stream-based Hebbian eigenfilter with GHA and a group of traditional PCA
algorithms, the computationally economical property of the proposed method was
demonstrated. The operation and memory counts of stream-based Hebbian eigenfilter
were obtained according to the algorithm shown in Table 2. The computational complexity of GHA was derived according to Table 1. Conventional PCA algorithms are
composed by covariance matrix calculation and eigenvalue decomposition of covariance matrix. For eigenvalue decomposition, three commonly used symmetric eigenvalue decomposition methods were taken into account for our comparison, which were
the orthogonal iteration [31], the symmetric QR algorithm [31] and the Jacobi method
[31]. Operation and memory counts for covariance matrix calculation and symmetric
matrix decomposition algorithms were derived according to standard texts on matrix
computation [31].
Algorithm implementation
The algorithm of stream-based eigenfilter was developed under Matlab R2009b. Matlab
built-in functions, princomp, was used as the conventional PCA routine. For evaluating
the performance of spike sorting using stream-based Hebbian eigenfilter and PCA,
NEO-based spike detection algorithm was developed using Matlab, and Matlab built-in
functions, kmeans, was used for K-means clustering.
Hardware implementation
Xilinx FPGA was used for hardware implementation and evaluation. The targeting
device is Xilinx Spartan6 FPGA (xc6slx75t). Xilinx System Generator was our hardware
design tool, which is a schematic based design tool. Working in Matlab Simulink environment makes System Generator easy for hardware-software co-design and hardware
verification. We obtained the hardware resources usage through Xilinx ISE tool. The
hardware power was obtained from Xilinx Xpower tool.
Both streaming and non-streaming Hebbian eigenfilter were implemented on the
FPGA. Figure 3 shows the architecture of hardware Hebbian eigenfilter. It is an example that the first three principal components are filtered. It consists “learning kernel”,
“system controller”, “mean calculator”, “interface” and “memory”. Memory block only
exists in the non-streaming structure. “System controller” controls the operation of the
whole system. “Learning kernel” performs learning operations and consists of arith metic units, storing units and switchers. “LT” stores the result of LT = LT yyT , “score”
x , “weight” stores the three synaptic weights. These synaptic
stores result of y = W
weights are updated concurrently. Shifters are used when multiplying a small learning
rate has to be performed. Switchers route the signals between arithmetic unit and storage elements. “Mean calculator” calculates mean of data before mean is ready. After
mean is ready, “mean calculator” subtracts mean from data and sends mean centered
data to “learning kernal”. In the non-streaming Hebbian eigenfilter, “interface” write
the input streaming data to the memory and read data from memory for mean calculation and Hebbian learning. In the stream-based Hebbian eigenfilter, “interface” directly
forwards the input data to “mean calculator”.
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Figure 3 The hardware architecture of Hebbian eigenfilter.
The data path for computing the score, y , and LT = LT yyT is illustrated by Figure 4
(a). The multipliers and accumulators (adders) implement the dot product between
input spikes and synaptic weights. The results of dot products are stored in the
“score”. After the scores are obtained, multipliers are re-used for calculating the lower
triangular matrix of yyT . The results are stored in the “LT”. Figure 4(b) shows the data
i . Updated results are stored in registers
path for updating the i-th synaptic weight, W
“Wi“.
Results and discussion
Accuracy evaluation
In general, thousands of spikes are used in PC training procedure [19]. In our evaluation, we suppose 1024 spikes are used for training. For stream-based method, we used
the first 1024 spikes (data set 1) for mean calculation and the following 1024 spikes
(data set 2) for Hebbian learning. Figure 5(a) and 5(b) show the evaluation results of
differences (errors) between mean vectors of the two data sets (defined by Eq. 2) and
deviations of PCs obtained by stream-based eigenfilter and PCA (defined by Eq. 3).
Clinical data and synthetic spikes from [27] were used in the evaluation. The average
error of mean vector is 3.7%. The average deviation of the first two PCs is 1.7%. From
the results we can see that the error of mean vector introduced by the streaming estimation is small. This small error of mean vector leads to small discrepancy in PCs.
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Figure 4 (a) The data path for calculating score
(b) The data path for updating synaptic weights,
x) and the lower triangular matrix yyT .
(y = W
i.
W
We further evaluated the performance of Hebbian-based spike sorting algorithm and
compared with that using conventional PCA. For stream-based Hebbian eigenfilter, we
let N equal to 1024, which is the number of spikes used for mean calculation and Hebbian learning. The initializing learning rate equals to 0.1 and the weights equal to 0.5.
It has been shown in the experiments that the convergence of the eigenfilter is relatively independent to the initial synaptic weights. However, the learning rates would
contribute to the speed of the convergence, as reported in [24]. Both true positive rate
and false positive rate of classification were considered in our evaluation, as shown in
Figure 6(a) and 6(b). The results show that stream-based Hebbian eigenfilter can
achieve nearly the same performance as PCA-based sorting in terms of the accuracy of
spike classification.
In addition, the noise immunity of the proposed method was studied. Synthetic spike
trains with various noise level and neurons (2 to 4) were generated by synthetic spike
tool [29]. Figure 7 shows the relationship between the true positive rate and SNR for
spike sorting algorithms using the stream-based Hebbian eigenfilter and Matlab builtin algorithm for PCA, princomp. Comparing Figure 7(a), (b) and 7(c), we can see that
at the same SNR level, the smaller the neuron number is, the better classification
results are. We can also see that there is little difference between stream-based
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Figure 5 Error evaluation of steam-based Hebbian eigenfilter when compared to PCA. (a) Errors for
mean calculation and, (b) principal components calculation. Benchmark #1 ~ #12 are obtained from [27],
#13 is clinical data from [27].
Hebbian eigenfilter and Matlab princomp function used for spike sorting. As a result,
stream-based eigenfilter has the same effect as other PCA algorithms in spike sorting
process. Figure 8 shows the relationship between the false positive rate and SNR for
spike sorting algorithms using stream-based Hebbian eigenfilter and Matlab built-in
PCA. The false positive rates of spike sorting using the stream-based eigenfilter and
Matlab princomp function are nearly the same. For both methods, the false positive
rate falls as the SNR increases.
Computational complexity
In this section, the computational complexity of stream-based Hebbian eigenfilter are
evaluated and compared with GHA and other conventional PCA algorithms in terms
of operation counts and memory consumption. Hebbian and conventional PCA algorithms are all based on matrix computations. The complexity of matrix computations
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Figure 6 (a) True positive rate and (b) false positive rate of spike sorting using PCA (Matlab
princomp) and stream-based Hebbian eigenfilter. Benchmarks #1 ~ #12 are obtained from[27].
is associated with the dimension of matrixes. Particularly, for spike feature extraction,
it is determined by the dimension of aligned neuronal spikes. In our evaluation, we
suppose the number of spikes for PCA training is 1024, each spike contains 64 samples, and the first two PCs are calculated.
Conventional PCA algorithms consist of covariance matrix calculation and the eigenvalue decomposition. Three most used eigenvalue decomposition algorithms were evaluated, including orthogonal iteration, QR method and Jacobi method. The three
benchmark algorithms are all based on some sort of iterative calculations. We assume
that these numerical methods can be converged in 8 iterations in our evaluation. The
operation counts of Hebbian eigenfilter and three numerical PCA algorithms are listed
in Table 3. The results show that Hebbian eigenfilter reduce 89.8% ~ 95.7% and 86.6% ~
93.4% addition and multiplication operations, respectively. Besides, Hebbian method
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Figure 7 Evaluation of spike sorting accuracy with varied SNR. Comparisons between PCA (Matlab
princomp) and stream-based Hebbian eigenfilter are based on (a) 2 neruons (b) 3 neruons (c) 4 neurons
cases.
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Figure 8 Evaluation of false positive rate of spike sorting with varied SNR. Comparisons between
stream-based Hebbian eigenfilter and PCA (Matlab princomp) are based on (a) 2 neruons (b) 3 neruons (c)
4 neurons cases.
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does not need division and square root operations, which are complex and costly for
hardware implementation.
Table 3 also lists the memory consumptions of GHA, stream-based eigenfilter and
conventional PCA algorithms. In order to estimate the memory requirement, we suppose that each sample is represented by 16 bits. Because of not requiring covariance
matrix and matrixes related to eigenvalue decomposition, GHA needs smaller memory
than conventional PCA algorithms. But, large size memory is still needed for mean calculation and the following zero-mean transformation. Through employing streambased processing that estimates the mean value by using the previous data, streambased Hebbian algorithm does not require the large memory for buffering neuronal
spikes for mean and zero-mean transformation. Thus, it consumes the smallest memory. Compared with GHAand PCA, around 99% memories can be reduced by the
stream-based eigenfilter.
Hardware evaluation
Both non-stream and stream based Hebbian eigenfilter were implemented on Xilinx
Spartan6 FPGA (xc6slx75t). Table 4 shows the area and performance of the hardware
Hebbian eigenfilter. The learning latency is the time needed to process one spike.
Logic consumption is the LUT (look-up-table), which is the basic logic block in FPGA,
consumed by the design. Memory consumption is the block RAM (BRAM) consumed
by the design, which is the basic memory block in FPGA. The results show that significant memory and power consumption reduction can be achieved by using the streaming approach. Compared with non-streaming eigenfilter, 92% BRAM and 67% power
consumption can be saved by streaming method.
Table 3 Comparison on computational complexity between PCA methods and Hebbian
eigenfilter
#Add.
#Multi.
#Div.
#Square root
#Memory
× 106
× 106
× 103
×103
(bits) × 106
Hebbian eigenfilter (HE)
0.46
0.59
0
0
1.05
0.0031
Stream-based HE (SHE)
0.46
0.59
0
0
Orthogonal iteration (OI) based PCA
4.51
4.39
0.016
0.016
1.18
QR method based PCA
4.77
4.75
1.1
0.57
1.25
Jacobi method based PCA
10.6
8.94
48.4
322
1.18
99.7%
Computational
OI vs SHE
89.8%
86.6%
100%
100%
complexity improvement
QR vs SHE
90.4%
87.6%
100%
100%
99.8%
(reduction rate)
Jacobi vs SHE
95.7%
93.4%
100%
100%
99.7%
Table 4 Area and performance comparison between FPGA-based Hebbi an eigenfilter
and PCA
Hebbian eigenfilter
Stream-based HE
PCA
Improvement
(HE)
(SHE)
[32]
(SHE vs PCA)
Number of slice
897
749
7722
10.3x
Number of BRAM
65
5
65
13x
Power (mW)
7.3
2.4
49.3
20.5x
Learning latency (μs )
5.6
5.6
42.4
7.6x
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Table 4 also compares the hardware performance between the FPGA-based Hebbian
eigenfilter and PCA hardware [32]. Hardware performances are varied if different technologies and devices are employed for the implementations. Especially, hardware performances using ASIC (application specific integrated circuit) and FPGAs are different
for a particular design. To obtain a fair comparison, we normalized the performance of
the ASIC-based PCA hardware [32] to FPGA equivalent and compared with our implementations. These would provide insightful quantitative evaluations between the different approaches in terms of hardware performance. But these results shouldn’t be
regarded as specifications of system performances.
Suppose the PCA hardware architectures have the same computing capability as the
Hebbian eigenfilter, under the same clock frequency latency will be proportional to the
computational complexity. Latency (or delay) results are reported in Table 4. The Hebbian eigenfilter approach has a significant advantage in delay that is 7.6 times faster
than the PCA hardware. This is critical to be employed in real-time spike sorting. The
Hebbian eigenfilter approach also has significant improvement in hardware resources.
Hardware logic resources can be significantly reduced by 10.3 times when compared to
the PCA hardware. Finally, we evaluated the power consumption. Results show that the
stream-based Hebbian eigenfilter have 20.5 times improvement when compared to the
PCA hardware implementations in terms of power consumption.
Conclusion
This paper presents a novel stream-based Hebbian eigenfilter for spike sorting. It calculates principal components of neuronal spikes based on an effective auto-associative
Hebbian learning, which is computationally economical. A stream-based computing
scheme is proposed to effectively reduce the memory requirements by utilizing the
pseudo-stationarity of neuronal spikes. Evaluation results show that the stream-based
eigenfilter is as accurate as conventional PCA methods for spike sorting. The computational complexity of the proposed method is ten times less than that of conventional
PCA. By utilizing the streaming method, 92% memory resources and 67% power consumption can be saved when compared with non-streaming eigenfilter. Compared with
FPGA-based PCA hardware, the proposed eigenfilter reduces logic resources and
power consumption by 10.3 and 20.5 times respectively. The new method enables realtime spike sorting for multi-channels neuro-physiological experiments and can be
further utilized by implantable systems for chronic diseases.
Endnotes
We follow a widely acceptable approach [33,34] to convert the ASIC design into FPGA
results. Particularly, FPGA implementation is 4.5 times slower than the corresponding
ASIC design. In terms of area, FPGA implementation is 21 times larger than equivalent
ASIC design in terms of area, and 128 logic counts in FPGAs equals to 0.82 mm2 in 90
nm CMOS technology [34]. Also, FPGA consumes 12 times more power than the
equivalent ASIC.
Acknowledgements
This work is supported by EPSRC grant EP/E044662/1, National Natural Science Foundation of China grant 61006021
and Beijing Natural Science Foundation grant 4112029. Chi-Sang Poon was supported by U.S. National Institutes of
Health grants HL067966 andRR028241.
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Author details
1
Tsinghua National Laboratory for Information Science and Technology, Institute of Microelectronics, Tsinghua
University, Beijing 100084, China. 2School of Electrical, Electronic and Computer Engineering, Newcastle University,
Newcastle upon Tyne NE47RU, UK. 3Institute of Neuroscience, Newcastle Biomedicine, Newcastle University, Newcastle
upon Tyne NE17RU, UK. 4Department of Computing Science and Mathematics University of Stirling, Stirling FK9 4LA,
UK. 5Harvard-MIT Division of Health Sciences and Technology, MIT, Cambridge MA 02139, USA.
Authors’ contributions
BY, TM and CSP proposed the idea. BY carried out the experiment, implemented the algorithm and hardware and
evaluated the algorithm and hardware. BY and TM drafted the manuscript. LS provided the tool for generating
synthetic spikes. TM, LS, YHS, XYL and CSP provided critical revision of the manuscript. TM and YHS supervised the
study. TM, CSP and XYL obtained the funding. Also, all the author read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Received: 21 December 2011 Accepted: 10 April 2012 Published: 10 April 2012
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doi:10.1186/1475-925X-11-18
Cite this article as: Yu et al.: Stream-based Hebbian eigenfilter for real-time neuronal spike discrimination.
BioMedical Engineering OnLine 2012 11:18.
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